Problem: A circle with circumference $8\pi$ has an arc with a $207^\circ$ central angle. What is the length of the arc? ${8\pi}$ ${207^\circ}$ $\color{#DF0030}{\dfrac{23}{5}\pi}$
Solution: The ratio between the arc's central angle $\theta$ and $360^\circ$ is equal to the ratio between the arc length $s$ and the circle's circumference $c$ $\dfrac{\theta}{360^\circ} = \dfrac{s}{c}$ $\dfrac{207^\circ}{360^\circ} = \dfrac{s}{8\pi}$ $\dfrac{23}{40} = \dfrac{s}{8\pi}$ $\dfrac{23}{40} \times 8\pi = s$ $\dfrac{23}{5}\pi = s$